AMC 12 2025a Problem 17

The polynomial $(z + i)(z + 2i)(z + 3i) + 10$ has three roots in the complex plane, where $i = \sqrt{-1}$. What is the area of the triangle formed by these three roots?

\textbf{(A)}~6 \textbf{(B)}~8 \textbf{(C)}~10 \textbf{(D)}~12 \textbf{(E)}~14